Web service non soap over SSL - How to do DUAL authentication

I am writing a web service which calls a 3rd party web service using HTTP POST (non SOAP) where DUAL authenitcation is enabled (both server & client certificates). I have both certificates and have an idea to send the client certificate with the web request.
Can anyone help me to understand how to use the server certificate here? Do we have to send it in the request (same way as client cert)? or any other method need to be written to validate the server cert?